Question

Calcule o valor de X. (HELP-ME)

Answer 1

a)
cos(60°)=$\frac{C.A.}{H} \Rightarrow \frac{1}{2} = \frac{6}{x} \Rightarrow x=6.2 \Rightarrow x=12$

b)
sen(30°)=\frac{C.O.}{H} \Rightarrow  \frac{1}{2} = \frac{4 \sqrt{3}}{x} \Rightarrow x=4 \sqrt{3}.2 \Rightarrow x=8 \sqrt{3} Rightarrow x=13,8564...

c)  $x1+x2=x$

$x1$ cateto adjacente de 45° e $x2$ cateto adjacente de 60°.

$tg(45°)= \frac{C.O.}{C.A.} \Rightarrow tg(45°)= \frac{15}{x1} \Rightarrow 1=\frac{15}{x1} \Rightarrow x1=15$

$tg(60°)= \frac{C.O.}{C.A.} \Rightarrow tg(60°)= \frac{15}{x2} \Rightarrow \sqrt{3} =\frac{15}{x2} \Rightarrow x2= \frac{15}{ \sqrt{3}} \Rightarrow$
$\Rightarrow x2= \frac{15.\sqrt{3}}{ \sqrt{3}. \sqrt{3}} \Rightarrow x2= \frac{15.\sqrt{3}}{ (\sqrt{3})^2} \Rightarrow x2= \frac{15.\sqrt{3}}{3} \Rightarrow x2=[tex] [tex]x=x1+x2 \Rightarrow x=15+5. \sqrt{3} \Rightarrow x=5.3+5. \sqrt{3} \Rightarrow x=5.(3+ \sqrt{3} )$